6 ms·

Good post. Somewhat related: Any good books/recommendations for those hoping to study post-school math on their own?

taliesinb 15y ago
Choose a path. What are you interested in? The theory of information? Ideas about space that go behind the flat plane of a piece of paper? How to communicate and co-operate securely when people might be eavesdropping and impersonating your allies? How to model various kinds of learning? How one studies the interacting strategies of military, economic, or biological adversaries? How complexity arises in simple systems? How sounds and images can be compressed? These are just examples, but each one of these topics will select a certain 'diet' of pure mathematics that will keep you well fed with cool ideas as well as 'in's to different fields. Although it does work for some people to just pick up a book on linear algebra and read it from cover to cover, I've never found that a very interesting or self-motivating way to learn. I think its better to hang one's knowledge on a tree of interlinked explorations.
- DharmaSoldat 15y ago
  I second that. My main side-project-esque interests involve AI and Computer Vision. Knowing that cleared up a lot of confusion as to what was 'best to learn'.
DharmaSoldat 15y ago
I graduated with Math 11 in highschool and never pursued it again to any extent until I was out of programming the first time and about 3 years into my culinary career. I decided to pick up calculus and linear algebra citing a lack of intellectual stimulation. I used the dummies books and augmented them with schaum's outlines (not easy studying). I got back into programming again, and although I didn't make it all the way through the first time, i've picked it up and have found the Demystifying series pretty good (better than the dummies books by a long shot in fact). These are also bolstered by other books I find that fell off the back of the internet truck. There's lots of great website for study notes and tutorials. One I like is Paul's Online Math Notes (http://tutorial.math.lamar.edu/ http://tutorial.math.lamar.edu/).
alfiejohn_ 15y ago
If you don't understand proofs, don't read any more maths books until you've read "Prove It": http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995 Even though you'll learn to read and write rigorous proofs with this book, it's requirements are high school maths and doesn't assume anything.
knotty66 15y ago
Khan Academy - not sure how far 'post school' it goes though. Try the exercises, definitely good for a refresher at least.
- taliesinb 15y ago
  It doesn't go very deep at all -- I've checked. It is pretty wide, though.
- taliesinb 15y ago
  Probably not a bad place to start is just iTunes U. There is some pretty cool stuff curated there -- I'm just delving into Andrew Ng's machine learning course.
GrangalanJr 15y ago
Here are some nice introductory ones: Mathematics: A Very Short Introduction (Tim Gowers): http://www.amazon.com/Mathematics-Short-Introduction-Timothy-Gowers/dp/0192853619 http://www.amazon.com/Mathematics-Short-Introduction-Timothy... The Language of Mathematics: Making the Invisible Visible (Keith Devlin): http://www.amazon.com/Language-Mathematics-Making-Invisible-Visible/dp/0805072543/ref=pd_sim_b_3 http://www.amazon.com/Language-Mathematics-Making-Invisible-... What is Mathematics?: An Elementary Approach to Ideas and Methods (Richard Courant): http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=pd_sim_b_3 http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-... They give brief but interesting glimpses into several areas of higher math, so they could help you decide what you want to pursue in more depth.

Choose a path. What are you interested in? The theory of information? Ideas about space that go behind the flat plane of a piece of paper? How to communicate and co-operate securely when people might be eavesdropping and impersonating your allies? How to model various kinds of learning? How one studies the interacting strategies of military, economic, or biological adversaries? How complexity arises in simple systems? How sounds and images can be compressed? These are just examples, but each one of these topics will select a certain 'diet' of pure mathematics that will keep you well fed with cool ideas as well as 'in's to different fields. Although it does work for some people to just pick up a book on linear algebra and read it from cover to cover, I've never found that a very interesting or self-motivating way to learn. I think its better to hang one's knowledge on a tree of interlinked explorations.

DharmaSoldat 15y ago
I second that. My main side-project-esque interests involve AI and Computer Vision. Knowing that cleared up a lot of confusion as to what was 'best to learn'.

DharmaSoldat 15y ago

I graduated with Math 11 in highschool and never pursued it again to any extent until I was out of programming the first time and about 3 years into my culinary career. I decided to pick up calculus and linear algebra citing a lack of intellectual stimulation. I used the dummies books and augmented them with schaum's outlines (not easy studying). I got back into programming again, and although I didn't make it all the way through the first time, i've picked it up and have found the Demystifying series pretty good (better than the dummies books by a long shot in fact). These are also bolstered by other books I find that fell off the back of the internet truck. There's lots of great website for study notes and tutorials. One I like is Paul's Online Math Notes (http://tutorial.math.lamar.edu/ http://tutorial.math.lamar.edu/).

alfiejohn_ 15y ago

If you don't understand proofs, don't read any more maths books until you've read "Prove It": http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995 Even though you'll learn to read and write rigorous proofs with this book, it's requirements are high school maths and doesn't assume anything.

knotty66 15y ago

Khan Academy - not sure how far 'post school' it goes though. Try the exercises, definitely good for a refresher at least.

taliesinb 15y ago
It doesn't go very deep at all -- I've checked. It is pretty wide, though.
taliesinb 15y ago
Probably not a bad place to start is just iTunes U. There is some pretty cool stuff curated there -- I'm just delving into Andrew Ng's machine learning course.

GrangalanJr 15y ago

Here are some nice introductory ones: Mathematics: A Very Short Introduction (Tim Gowers): http://www.amazon.com/Mathematics-Short-Introduction-Timothy-Gowers/dp/0192853619 http://www.amazon.com/Mathematics-Short-Introduction-Timothy... The Language of Mathematics: Making the Invisible Visible (Keith Devlin): http://www.amazon.com/Language-Mathematics-Making-Invisible-Visible/dp/0805072543/ref=pd_sim_b_3 http://www.amazon.com/Language-Mathematics-Making-Invisible-... What is Mathematics?: An Elementary Approach to Ideas and Methods (Richard Courant): http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=pd_sim_b_3 http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-... They give brief but interesting glimpses into several areas of higher math, so they could help you decide what you want to pursue in more depth.